Lofting between edges
A current "lazy" approach to this. might be:



I use a few VD nodes here to emphasize the original Quad outlines (light blue), and the resulting interpolated outer edge (red). Note that the Plane (Mesh) Object has a Vertex order which is [0, 1, 3, 2], and we need both Verts and Edges to order the vertices (using Vector Sort) for the "connected" algorithm to get [0, 1, 2, 3].

The Smooth Lines node offers "Weights" input. When using the slider all verts are treated the same, but you can pass it a list of values (ranging from 0 to 1) to effect vertices uniquely.



I feel perhaps that this does not provide a full solution to your question, but sometimes even a partial answer can be useful.